2. Basic Calculations

Table of Content

  1. Volumes and Strokes
  2. Slug Calculations
  3. Accumulator Capacity — Usable Volume Per Bottle
  4. Bulk Density of Cuttings (Using Mud Balance)
  5. Drill String Design (Limitations)
  6. Ton-Mile (TM) Calculations
  7. Cementing Calculations
  8. Weighted Cement Calculations
  9. Calculations for the Number of Sacks of Cement Required
  10. Calculations for the Number of Feet to Be Cemented
  11. Setting a Balanced Cement Plug
  12. Differential Hydrostatic Pressure Between Cement in the Annulus and Mud Inside the Casing
  13. Hydraulicing Casing
  14. Depth of a Washout
  15. Lost Returns — Loss of Overbalance
  16. Stuck Pipe Calculations
  17. Calculations Required for Spotting Pills
  18. Pressure Required to Break Circulation

2.3 Accumulator Capacity — Usable Volume Per Bottle

Usable Volume Per Bottle

NOTE: The following will be used as guidelines:
Volume per bottle = 10 gal
Pre-charge pressure = 1000 psi
Maximum pressure = 3000 psi
Minimum pressure remaining after activation = 1200 psi
Pressure gradient of hydraulic fluid = 0.445 psi/ft

Boyle’s Law for ideal gases will be adjusted and used as follows:

P1 V1 = P2 V2

Surface Application

Step 1 Determine hydraulic fluid necessary to increase pressure from pre-charge to minimum:

P1 V1 = P2 V2
1000 psi × 10 gal = 1200 psi × V2
10000 1200 = V 2
V2 = 8.33 The nitrogen has been compressed from 10.0 gal to 8.33 gal.
10.0 − 8.33 = 1.67 gal of hydraulic fluid per bottle.
NOTE: This is dead hydraulic fluid. The pressure must not drop below this minimum value.

Step 2 Determine hydraulic fluid necessary to increase pressure from pre-charge to maximum:

P1 V1 = P2 V2
1000 psi × 10 gal = 3000 psi × V2
10000 3000 = V 2
V2 = 3.33 The nitrogen has been compressed from 10.0 gal to 3.33 gal.
10.0 − 3.33 = 6.67 gal of hydraulic fluid per bottle.

Step 3 Determine usable volume per bottle:

Useable vol./bottle = Total hydraulic fluid/bottle — Dead hydraulic fluid/bottle
Useable vol./bottle = 6.67 − 1.67
Useable vol./bottle = 5.0 gallons

Subsea Applications

In subsea applications the hydrostatic pressure exerted by the hydraulic fluid must be compensated for in the calculations.

Example: Same guidelines as in surface applications:
Water depth = 1000 ft
Hydrostatic pressure of hydraulic fluid = 445 psi

Step 1 Adjust all pressures for the hydrostatic pressure of the hydraulic fluid:

Pre-charge pressure = 1000 psi + 445 psi = 1445 psi
Minimum pressure = 1200 psi + 445 psi = 1645 psi
Maximum pressure = 3000 psi + 445 psi = 3445 psi

Step 2 Determine hydraulic fluid necessary to increase pressure from pre-charge to minimum:

P1 V1 = P2 V2
1445 psi × 10 gal = 1645 psi × V2
14450 1645 = V 2
V2 = 8.78 gal
10.0 − 8.78 = 1.22 gal of dead hydraulic fluid

Step 3 Determine hydraulic fluid necessary to increase pressure from pre-charge to maximum:

P1 V1 = P2 V2
1445 psi × 10 gal = 3445 psi × V2
14450 3445 = V 2
V2 = 4.19 gal
10.0 − 4.19 = 5.81 gal of hydraulic fluid per bottle

Step 4 Determine useable fluid volume per bottle:

Useable vol./bottle = Total hydraulic fluid/bottle − Dead hydraulic fluid/bottle
Useable vol./bottle = 5.81 − 1.22
Useable vol./bottle = 4.59 gallons

Accumulator Pre-charge Pressure

The following is a method of measuring the average accumulator pre-charge pressure by operating the unit with the charge pumps switched off:

P, psi = vol. removed, bbl total acc. vol., bbl × Pf × Ps Ps − Pf

where P = average pre-charge pressure, psi
Pf = final accumulator pressure, psi
Ps = starting accumulator pressure, psi

Example: Determine the average accumulator pre-charge pressure using the following data:
Starting accumulator pressure (Ps) = 3000 psi
Final accumulator pressure (Pf) = 2200 psi
Volume of fluid removed = 20 gal
Total accumulator volume = 180 gal

P, psi = 20 ÷ 180 × ((2200 × 3000) ÷ (3000 − 2200))
P, psi = 0.1111 × (6,600,000 ÷ 800)
P, psi = 0.1111 × 8250
P = 917psi

⬆ Table of Content